The present paper discusses #-rewriting systems, which represent simple language-defining devices that combine both automata and grammars. Indeed, like automata, they use finitely many states without any nonterminals; on the other hand, like grammars, they generate languages. The paper introduces n-right-linear #-rewriting systems and characterize the infinite hierarchy of language families defined by m-parallel n-right-linear simple matrix grammars. However, it also places some trivial restrictions on rewriting in these systems and demonstrates that under these restrictions, they generate only the family of right-linear languages. In its conclusion, this paper suggests some variants of #-rewriting systems.